OPTIMAL IV ESTIMATION OF SYSTEMS WITH STOCHASTIC REGRESSORS AND VAR DISTURBANCES WITH APPLICATIONS TO DYNAMIC SYSTEMS

This paper considers the general problem of Feasible Generalized Least Squares Instrumental Variables (FGLS IV) estimation using optimal instruments. First we summarize the sufficient conditions for the FGLS IV estimator to be asymptotically equivalent to an optimal GLS IV estimator. Then we specialize to stationary dynamic systems with stationary VAR errors, and use the sufficient conditions to derive new moment conditions for these models. These moment conditions produce useful IVs from the lagged endogenous variables, despite the correlation between errors and endogenous variables. This use of the information contained in the lagged endogenous variables expands the class of IV estimators under consideration and thereby potentially improves both asymptotic and small-sample efficiency of the optimal IV estimator in the class. Some Monte Carlo experiments compare the new methods with those of Hatanaka (1976). For the DGP used in the Monte Carlo experiments, asymptotic efficiency is strictly improved by the new IVs, and experimental small-sample efficiency is improved as well.     

OPTIMAL IV ESTIMATION OF SYSTEMS WITH STOCHASTIC REGRESSORS AND VAR DISTURBANCES WITH APPLICATIONS TO DYNAMIC SYSTEMS

This paper considers the general problem of Feasible Generalized Least Squares Instrumental Variables (FGLS IV) estimation using optimal instruments. First we summarize the sufficient conditions for the FGLS IV estimator to be asymptotically equivalent to an optimal GLS IV estimator. Then we specialize to stationary dynamic systems with stationary VAR errors, and use the sufficient conditions to derive new moment conditions for these models. These moment conditions produce useful IVs from the lagged endogenous variables, despite the correlation between errors and endogenous variables. This use of the information contained in the lagged endogenous variables expands the class of IV estimators under consideration and thereby potentially improves both asymptotic and small-sample efficiency of the optimal IV estimator in the class. Some Monte Carlo experiments compare the new methods with those of Hatanaka (1976). For the DGP used in the Monte Carlo experiments, asymptotic efficiency is strictly improved by the new IVs, and experimental small-sample efficiency is improved as well.     

SHRINKAGE, PRETEST AND ABSOLUTE PENALTY ESTIMATORS IN PARTIALLY LINEAR MODELS

We consider a partially linear model in which the vector of coefficients β in the linear part can be partitioned as ( β ₁, β ₂) , where β ₁ is the coefficient vector for main effects (e.g. treatment effect, genetic effects) and β ₂ is a vector for ‘nuisance’ effects (e.g. age, laboratory). In this situation, inference about β ₁ may benefit from moving the least squares estimate for the full model in the direction of the least squares estimate without the nuisance variables (Steinian shrinkage), or from dropping the nuisance variables if there is evidence that they do not provide useful information (pretesting). We investigate the asymptotic properties of Stein‐type and pretest semiparametric estimators under quadratic loss and show that, under general conditions, a Stein‐type semiparametric estimator improves on the full model conventional semiparametric least squares estimator. The relative performance of the estimators is examined using asymptotic analysis of quadratic risk functions and it is found that the Stein‐type estimator outperforms the full model estimator uniformly. By contrast, the pretest estimator dominates the least squares estimator only in a small part of the parameter space, which is consistent with the theory. We also consider an absolute penalty‐type estimator for partially linear models and give a Monte Carlo simulation comparison of shrinkage, pretest and the absolute penalty‐type estimators. The comparison shows that the shrinkage method performs better than the absolute penalty‐type estimation method when the dimension of the β ₂ parameter space is large.     

CAUSAL GRAPHICAL MODELS IN SYSTEMS GENETICS: A UNIFIED FRAMEWORK FOR JOINT INFERENCE OF CAUSAL NETWORK AND GENETIC ARCHITECTURE FOR CORRELATED PHENOTYPES

Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenotypes. Randomization of alleles during meiosis and the unidirectional influence of genotype on phenotype allow the inference of QTLs causal to phenotypes. Causal relationships among phenotypes can be inferred using these QTL nodes, enabling us to distinguish among phenotype networks that would otherwise be distribution equivalent. We jointly model phenotypes and QTLs using homogeneous conditional Gaussian regression models, and we derive a graphical criterion for distribution equivalence. We validate the QTLnet approach in a simulation study. Finally, we illustrate with simulated data and a real example how QTLnet can be used to infer both direct and indirect effects of QTLs and phenotypes that co-map to a genomic region.     

APPLICATIONS OF ROBUST ESTIMATION FOR VARIANCE COMPONENTS MODELS:THE DETECTION OF MAJOR GENE EFFECTS IN FINGER RIDGE COUNTS IN NORMAL AND FRAGILE X FAMILIES

A diagnostic technique is proposed to detect major gene effects and other systematic departures from a model for the trait means in the presence of outliers. The technique is based on the examination of residuals from fitting variance components models to quantitative pedigree data using robust statistical procedures. The approach is demonstrated using the total ridge count and ridge count of the middle finger from 54 extended families affected with the Fragile X syndrome, and a sample of 217 normal pedigrees.     

INVENTORY PROCESSES: QUASI-REGENERATIVE PROPERTY,PERFORMANCE EVALUATION,AND SENSITIVITY ESTIMATION VIA SIMULATION

We consider a single-commodity, discrete-time, multiperiod (s, S)-policy inventory model with backlog. The cost function may contain holding, shortage, and fixed ordering costs. Holding and shortage costs may be nonlinear. We show that the resulting inventory process is quasi-regenerative, i.e., admits a cycle decomposition and indicates how to estimate the performance by Monte Carlo simulation. By using a conditioning method, the push-out technique, and the change-of-measure method, estimates of the whole response surface (i.e., the steady-state performance in dependence of the parameters s and S) and its derivatives can be found. Estimates for the optimal (s, S) policy can be calculated then by numerical optimization.